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We perform the first tight convergence analysis of the gradient method with varying step sizes when applied to smooth hypoconvex (weakly convex) functions.
Performance of first-order methods for smooth convex minimization: a novel approach
Yoel Drori and Marc Teboulle · 2014
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Introductory Lectures on Convex Optimization: A Basic Course
Yurii Nesterov · 2014
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Convergence Rate Analysis of Several Splitting Schemes
Damek Davis and Wotao Yin · 2016
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On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions
Etienne de Klerk, François Glineur, and Adrien B. Taylor · 2017
Earlier work this paper cites.
The exact information-based complexity of smooth convex minimization
Yoel Drori · 2017
Cited alongside, same era.
Convex interpolation and performance estimation of first-order methods for convex optimization
Adrien Taylor · 2017
Cited alongside, same era.
Performance estimation toolbox (PESTO): Automated worst-case analysis of first-order optimization methods
Adrien B. Taylor, Julien M. Hendrickx, and François Glineur · 2017
Cited alongside, same era.
Smooth strongly convex interpolation and exact worst-case performance of first-order methods
Adrien B. Taylor, Julien M. Hendrickx, and François Glineur · 2017
Cited alongside, same era.
The complexity of finding stationary points with stochastic gradient descent
Yoel Drori and Ohad Shamir · 2020
Later among the works it cites.
The exact worst-case convergence rate of the gradient method with fixed step lengths for l-smooth functions
Hadi Abbaszadehpeivasti, Etienne de Klerk, and Moslem Zamani · 2021
Later among the works it cites.
Optimizing the efficiency of first-order methods for decreasing the gradient of smooth convex functions
Donghwan Kim and Jeffrey A. Fessler · 2021
Later among the works it cites.
Pepit: computer-assisted worst-case analyses of first-order optimization methods in Python, 2022
Baptiste Goujaud, Céline Moucer, François Glineur, Julien Hendrickx, Adrien Taylor, and Aymeric Dieuleveut · 2022
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